x^2+1=-8x

Solution for x^2+1=-8x equation:

x^2+1=-8x

We move all terms to the left:

x^2+1-(-8x)=0

We get rid of parentheses

x^2+8x+1=0

a = 1; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·1·1
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{15}}{2*1}=\frac{-8-2\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{15}}{2*1}=\frac{-8+2\sqrt{15}}{2}
$